Deductive and Inductive Logic

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Deductive Logic

Deductive Logic is the method of non contradictory identification. It is based on the classical axioms of Aristotelean logic. Deductive arguments are akin to mathematical equations: they present a series of categories or definitions in a series of equivalencies. For this reason, the conclusion of a deductive argument necessarily follows from its premises, in the same way that 4 follows from the "premise" of 2+2=. In the opinion of this author, the most elegant form of a deductive argument is Aristotle's syllogistic logic, or classical deductive logic.

Generally, it is held by logicians that deductive arguments work from general rules to specific conclusions. For example, consider this categorical syllogism:

All humans are mortal
Socrates is human
Therefore, Socrates is mortal

This syllogism works from a general rule: "all humans are mortal" to a specific conclusion: "Socrates is mortal". However, it is not necessary that deductive arguments move from general or universal statements, to specific or particular statements, for example, a deductive argument can work from particular premises, consider this disjunctive syllogism:

If Socrates is a human, then Socrates is mortal
Socrates is a human
Therefore, Socrates is mortal

We can call a deductive logical system an a priori system. This means that we can make up such a system without any observation or experimental examination.We can create a set of categories like squares or circles or letters, and a set of self consistent rules that follow a set of definitions, all without having to ever experience such "things".

Philosophers like to say that a "brain in vat" set apart from the rest of the universe could create an a priori system.

Inductive Logic

Inductive arguments are not like mathematical equations at all, they are akin to predictions - i.e. they are probable claims. They don't work with abstract entities like categories or definitions, they work with empirical claims from the physical world outside of our imaginations. The "real world" outside of our imaginations does not give us a set of abstract categories, it gives us a set of imprecise entities that exist along an imprecise continuum. For this reason, inductive arguments do not posses the certainty of deductive arguments. All inductive arguments are uncertain and open to questioning.

"Don't speak to me in absolutes, the evidence IS contestable!"
(Dr Zaius to Cornelius, regarding archeological (inductive) evidence, in Planet of the Apes - one of the few instances where Hollywood's take on science was right on the money.)

When dealing with inductive arguments, we can only say that the conclusion is likely to follow from the premises.

Some logicians hold that induction works from "particulars to general rules of inference"

I have seen many crows
All of them were black
It stands to reason that all crows are probably black

But again, inductive arguments can work from general rules to particular conclusions, or from particular premises to particular conclusions

Examples of inductive arguments would include arguments from analogy (which are always imperfect), generalizations from a sample to a group,), and, from causal inferences (from cause to effect OR from effect to cause or arguments based on signs or evidence. If you are a fan of the famous sleuth Sherlock Holmes, who often worked from signs and evidence, you will quickly realize from this definition that Holmes was a famous INductiontionist, not, as he himself often claimed, a great deductionist!

Abduction

As a side note for later study (section to be added later), the logician Charles S. Peirce holds that we should also consider "abduction", which is defined as follows: "Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea" (Peirce, 1903:CP 5.171).

Review: Categories vs A Continuum

It was the great thinker Galileo who explicated upon the limitations of Aristotle's categorical paradigm that were first noted by his contemporaries, the Sophists: we can create abstract categories like squares, and set up deductive arguments that speak about equivalenceis between such categories, but categories have no real world correlate - we live in a changing world of impreciseness, where everything falls somewhere along a continuum. This is not to say that deduction has no use, after all, geometry also deals with categories like circles and squares, and is quite useful. It is only to say that while deductive arguments give us 'certain' conclusions, we cannot apply these certain conclusions to the real world without error.